Geometric Sequence Calculator
Calculate the sum of first n terms and the nth term of geometric sequence
Result
Calculation Steps
Geometric Sequence Calculator Introduction
A geometric sequence is a sequence in which the ratio between any two consecutive terms is constant; this constant ratio is called the common ratio. Geometric sequences are widely applied in mathematics, physics, finance, and other fields, such as compound interest calculations, radioactive decay, and population growth models.
Enter the first term (a₁), the common ratio (r), and the number of terms (n). The result will display the sum of the first n terms and the value of the nth term.
Geometric Sequence Formulas
1. General Term Formula
an = a1 × rn-1
2. Sum of the First n Terms Formula
When r ≠ 1: Sn = a1(1 - rn) / (1 - r)
When r = 1: Sn = n × a1
3. Sum of an Infinite Series Formula
When |r| < 1: S = a1 / (1 - r)